In particle accelerators, the motion of particle bunches at low energy is typically dominated by space-charge effects. For space-charge dominated particle beams (e.g. as found in injectors), it is not possible to operate particle accelerators in conventional ways to fully preserve the six-dimensional (6D) brightness of the bunch and approach the theoretical brightness limit.
Typically, radio frequency (RF) structures are used to either bunch or accelerate the particle bunches independently, which modifies (to the 1St order) 2D longitudinal phase space or 4D transverse phase space respectively. In order to preserve the 6D brightness of highly space-charge dominated beams, RF cavities must be operated in a way such that both bunching and acceleration occur simultaneously and optimally in such a manner that brightness is not destroyed. This process can be repeated in subsequent cavities with varying degrees of bunching/accelerating until the bunch is no longer space-charge dominated. The geometry, gradient and phase of the cavities are all required to optimally preserve bunch brightness and approach the brightness limit.
Accordingly, it would be advantageous to provide a method for operating RF cavities in such a manner that bunching and acceleration occur simultaneously and the six-dimensional brightness of the bunch is preserved.